Bài tập: 1. CMR: $cos(a+b).cos(a-b)=cos^2a-sin^2a$ 2. CMR: $\frac{1-cosx+cos2x}{sin2x-sinx}=cotx$

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1. 1.

   `cos(a+b).cos(a-b)`

   `=(cosa.cosb-sina.sinb).(cosa.cosb+sina.sinb)`

   `=cos^2a.cos^2b-sin^2a.sin^2b`

   `=cos^2b.(1-sin^2a)-sin^2a.(1-cos^2b)`

   `=cos^2b-cos^2b.sin^2a-sin^2a+cos^2b.sin^2a`

   `=cos^2b-sin^2a` (đpcm)

   2.

   `\frac{1-cosx+cos2x}{sin2x-sinx}`

   `=\frac{1-cosx+2cos^2x-1}{2.sinx.cosx-sinx}`

   `=\frac{cosx(2cosx-1)}{sinx(2cosx-1)}`

   `=\frac{cosx}{sinx}=cotx` (đpcm)

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